Eigenvalue problems

• An Updated Set of Nonlinear Eigenvalue Problems (with G. M. Negri Porzio and F. Tisseur). MIMS EPrint 2019.5, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, March 2019. 12 pp.
• NLEVP: A Collection of Nonlinear Eigenvalue Problems (with Timo Betcke, Volker Mehrmann, Christian Schroder and Françoise Tisseur), ACM Trans. Math. Software, 39(2):7:1-7:28, 2013. Published version.
• Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD (with Yuji Nakatsukasa), SIAM J. Sci. Comp. 35 (3): A1325-A1349, 2013. MATLAB codes at MATLAB Central File Exchange;
• A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems (with Laurence Grammont and Françoise Tisseur), Linear Algebra Appl. 435(3):623-640, 2011. Published version.
• Definite Matrix Polynomials and their Linearization by Definite Pencils (with D. Steven Mackey and Françoise Tisseur), SIAM J. Matrix Anal. Appl. 31(2), 478-502, 2009.
• An Improved Arc Algorithm for Detecting Definite Hermitian Pairs (with Chun-Hua Guo and Françoise Tisseur), SIAM J. Matrix Anal. Appl. 31(3), 1131-1151, 2009.
• Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems (with Chun-Hua Guo and Françoise Tisseur), SIAM J. Matrix Anal. Appl., 30(4):1593-1613, 2009.
• Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems (with D. Steven Mackey, Françoise Tisseur and Seamus D. Garvey), Internat. J. Numer. Methods Eng., 73(3):344-360, 2008. Published version.
• Backward Error of Polynomial Eigenproblems Solved by Linearization (with Ren-Cang Li and Françoise Tisseur), SIAM J. Matrix Anal. Appl., 29(4):1218-1241, 2007.
• Symmetric Linearizations for Matrix Polynomials (with D. Steven Mackey, Niloufer Mackey and Françoise Tisseur), SIAM J. Matrix Anal. Appl., 29(1):143-159, 2006.
• The Conditioning of Linearizations of Matrix Polynomials (with D. Steven Mackey, and Françoise Tisseur), SIAM J. Matrix Anal. Appl., 28(4): 1005-1028, 2006.
• Bounds for Eigenvalues of Matrix Polynomials (with Françoise Tisseur), Linear Algebra Appl., 358:5-22, 2003.
• Detecting a Definite Hermitian Pair and a Hyperbolic or Elliptic Quadratic Eigenvalue Problem, and Associated Nearness Problems (with Françoise Tisseur and Paul Van Dooren), Linear Algebra Appl., 351-352:455-474, 2002.
• More on Pseudospectra for Polynomial Eigenvalue Problems and Applications in Control Theory (with Françoise Tisseur ), Linear Algebra Appl., 351-352:435-453, 2002.
• Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications (with Françoise Tisseur ), SIAM J. Matrix Anal. Appl. 23(1): 187-208, 2001.
• Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem (with Philip Davies and Françoise Tisseur ), SIAM J. Matrix Anal. Appl. 23(2): 472-493, 2001.
• QR Factorization with Complete Pivoting and Accurate Computation of the SVD , Linear Algebra Appl., 309:153-174, 2000.
• The Nearest Definite Pair for the Hermitian Generalized Eigenvalue Problem (with Sheung Hun Cheng), Linear Algebra Appl., 302-303, 63-76, 1999.
• Modifying the Inertia of Matrices Arising in Optimization (with Sheung Hun Cheng), Linear Algebra Appl., 275-276:261-279, 1998.
• Structured Backward Error and Condition of Generalized Eigenvalue Problems (with Des Higham ), SIAM J. Matrix Anal. Appl., 20(2):493-512, 1998.
• Computing the Field of Values and Pseudospectra Using the Lanczos Method with Continuation (with Thierry Braconnier), BIT, 36(3):422-440, 1996.
• A New Parallel Algorithm for Computing the Singular Value Decomposition (with Pythagoras Papadimitriou), in J. G. Lewis, editor, Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, pages 80-84. Society for Industrial and Applied Mathematics, Philadelphia, 1994.
• Parallel Singular Value Decomposition via the Polar Decomposition (with Pythagoras Papadimitriou), Numerical Analysis Report No. 239, Manchester Centre for Computational Mathematics, Manchester, England, Oct. 1993.